(9x+5)*(4x+5)=125*x

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Solution for (9x+5)*(4x+5)=125*x equation: 


Simplifying
(9x + 5)(4x + 5) = 125x

Reorder the terms:
(5 + 9x)(4x + 5) = 125x

Reorder the terms:
(5 + 9x)(5 + 4x) = 125x

Multiply (5 + 9x) * (5 + 4x)
(5(5 + 4x) + 9x * (5 + 4x)) = 125x
((5 * 5 + 4x * 5) + 9x * (5 + 4x)) = 125x
((25 + 20x) + 9x * (5 + 4x)) = 125x
(25 + 20x + (5 * 9x + 4x * 9x)) = 125x
(25 + 20x + (45x + 36x2)) = 125x

Combine like terms: 20x + 45x = 65x
(25 + 65x + 36x2) = 125x

Solving
25 + 65x + 36x2 = 125x

Solving for variable 'x'.

Reorder the terms:
25 + 65x + -125x + 36x2 = 125x + -125x

Combine like terms: 65x + -125x = -60x
25 + -60x + 36x2 = 125x + -125x

Combine like terms: 125x + -125x = 0
25 + -60x + 36x2 = 0

Factor a trinomial.
(5 + -6x)(5 + -6x) = 0


Subproblem 1
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333

Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {0.8333333333, 0.8333333333}

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